Neural-network quantum state tomography

Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan; Troyer, Matthias; Melko, Roger G.; Carleo, Giuseppe

doi:10.1038/s41567-018-0048-5

Cited by 825 publications

(654 citation statements)

References 32 publications

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“…Actually, with increasingly so-phisticated experiments, the limitation of existing semiclassical methods based on FPI for reproducing and explaining some quantum phenomena has been becoming increasingly evident due to the limited amount of paths, especially for the new attosecond measurements where a series of high-resolution photoelectron spectra with different pump-probe delays are needed to obtain attosecond time-resolved movies of electrons [25][26][27][28][29][30][31][32].Since the game Go was mastered by deep neural networks (DNNs), deep learning (DL) has received extensive attention [33,34]. Recently, this technique has powered many fields of science, including planning chemical syntheses [35], acceleration of super-resolution localization microscopy and nudged elastic band calculations [36][37][38][39], classifying scientific data [40,41], solving highdimensional problems in condensed matter systems [42][43][44][45][46][47][48], reconstructing the shape of ultrashort pulses [49], and so on. However, to our knowledge, its power in strong-field physics has not yet been excavated.…”

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confidence: 99%

Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics

et al. 2020

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Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view. However, the complete characterization of quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose deep-learning-performed strong-field Feynman's formulation with pre-classification scheme which can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build up a bridge between deep learning and strong-field physics through the Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science, and shed a new light on the quantum-classical correspondence.The wave function and the temporal evolution contain all information of quantum physics. However, they might be possibly the hardest to grasp in the classical world. Seventy years ago, Feynman proposed a path integral approach which has been viewed as the "sum over paths or histories" version of quantum mechanics, i.e. the wave function can be represented as a coherent superposition of contributions of all possible spatio-temporal paths [1,2]. Even though the Feynman's path integral (FPI) has been considered as the most fundamental way to interpret the quantum mechanics and answer what is the nature of measurements, the complete characterization of quantum wavepacket with all possible paths is formidable due to track ergodicity. Typically, only a very limited amount of paths could be accessed, and therefore only a reduced amount of information of quantum wavepacket could be obtained in different approximation methods so far.The development history of semiclassical methods based on FPI in strong-field physics, from the strong-field approximation (SFA) to the Coulomb corrected strongfield approximation (CCSFA) and quantum trajectory Monte Carlo methods, also proves that the more trajectories have been adopted, the more information could be extracted . As a result, despite of the notable success of these methods, there still exist a large number of unexplored regimes, including the open question about whether one could truly achieve the quantumclassical correspondence. Actually, with increasingly so-phisticated experiments, the limitation of existing semiclassical methods based on FPI for reproducing and explaining some quantum phenomena has been becoming increasingly evident due to the limited amount of paths, especially for the new attosecond measurements where a series of high-resolution photoelectron spectra with different pump-probe delays are needed to obtain attosecond time-resolved movies of electrons [25][26][27][...

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confidence: 99%

Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics

et al. 2020

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“…From the work by Torlai and colleagues, for a pure quantum state, the neural network tomography works as follows. To reconstruct an unknown state

| Ψ ⟩

, we first perform a collection of measurements

{{boldv}^{(i)}}

i = 1, \dots, N

and therefore obtain the probabilities

p_{i} false(v^{false(i false)} false) = {| false⟨ v^{false(i false)} false| normalΨ false⟩ |}^{2}

.…”

Section: Density Operators Represented By Neural Networkmentioning

confidence: 99%

Quantum Neural Network States: A Brief Review of Methods and Applications

et al. 2019

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One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

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“…Meanwhile, there are many recent works combining ML techniques with quantum information tools . These include expressing and witnessing quantum entanglement by artificial neural networks (ANN), analyzing and restructuring a quantum state by restricted Boltzmann machines (RBM), as well as detecting quantum change points, and learning Hamiltonians by Bayesian inference . Meanwhile, many quantum ML algorithms have already been applied in different experimental systems, such as photonics and nuclear magnetic resonance (NMR) systems.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of a Photonic Qubit State with Reinforcement Learning

Albarrán-Arriagada

Retamal

et al. 2019

Adv Quantum Tech

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An experiment is performed to reconstruct an unknown photonic quantum state with a limited amount of copies. A semiquantum reinforcement learning approach is employed to adapt one qubit state, an “agent,” to an unknown quantum state, an “environment,” by successive single‐shot measurements and feedback, in order to achieve maximum overlap. The experimental learning device herein, composed of a quantum photonics setup, can adjust the corresponding parameters to rotate the agent system based on the measurement outcomes “0” or “1” in the environment (i.e., reward/punishment signals). The results show that, when assisted by such a quantum machine learning technique, fidelities of the deterministic single‐photon agent states can achieve over 88% under a proper reward/punishment ratio within 50 iterations. This protocol offers a tool for reconstructing an unknown quantum state when only limited copies are provided, and can also be extended to higher dimensions, multipartite, and mixed quantum state scenarios.

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Neural-network quantum state tomography

Cited by 825 publications

References 32 publications

Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics

Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics

Quantum Neural Network States: A Brief Review of Methods and Applications

Reconstruction of a Photonic Qubit State with Reinforcement Learning

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